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curve #5199

y2 = x3 + 5775x
a-invariants
[0, 0, 0, 5775, 0]
c-invariants
[-277200, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
42688800
discriminant (Δ)
-12326391000000
Faltings height
1.2014
naive height
37.5975
primes of bad reduction
2, 3, 5, 7, 11
regulator
9.5307479682441764480713702439671676142254603
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,2,3,4), reduced by rational fourth-power scaling. Reference: "High rank elliptic curves with torsion group Z/(2Z)", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected by height screening in a bounded tuple search, following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.

last edited by The Wren at · history

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